Numerical investigations of small-amplitude disturbances in a boundary layer with impinging shock wave at Ma=4.8

Abstract

The stability behavior of a laminar boundary layer with shock boundary layer interaction and small amplitude disturbances is investigated by linear stability theory and direct numerical simulation. By a complex interaction of several physical properties, the impinging shock wave locally influences stability behavior of the boundary layer, dependent on its shock strength, applied disturbance frequency, and disturbance propagation angle with respect to the flow direction (obliqueness angle). Due to the displacement of the boundary layer near shock impingement and the according Reynolds number effect in this area, the boundary layer is locally destabilized. The displacement of the boundary layer also produces an increase of the thickness of local regions of relative supersonic speed, which promotes second mode instability. For the results obtained by direct numerical simulation nonparallel effects could be identified and quantified. Taking these nonparallel effects into account, linear stability theory is able to represent the stability behavior of wall distant disturbance amplitude maxima having small obliqueness angles for the cases investigated here. For larger obliqueness angles and disturbance amplitudes at or close to the wall the agreement between linear stability theory and direct numerical simulation declines considerably.